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Find the interval in which f(x) is increasing
f(x) = ∫ex(x-1)(x-2) dx
Limit is from 0 to x.

Lovey , 10 Years ago
Grade 12
anser 1 Answers
Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

f(x) = \int_{0}^{x}e^{t}(t-1)(t-2)dt
Using Newton-Leibniz formula, we have
f'(x) = e^{x}(x-1)(x-2)
f(x) is increasing in the interval
f'(x)> 0
e^{x}(x-1)(x-2)> 0
exis always +ve for all x.
(x-1)(x-2)> 0
By wavy crve method, we have
x\in R - [1, 2]

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